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20 October, 21:47

If the sum of the squares of nonnegative real numbers a, b, and c is 39, and ab + bc + ca = 21, then what is the sum of a, b, and c?

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  1. 21 October, 00:46
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    Step-by-step explanation:

    a² + b² + c² = 39

    ab + bc + ca = 21

    (a + b + c) ² = a² + b² + c² + 2[ab + bc + ca]

    (a + b + c) ² = 39 + 2*21

    = 39 + 42

    (a + b + c) ² = 81

    a + b + c = √81 = √9*9

    a + b + c = 9
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